Preheat oven to 325 degrees F. Grease wells of donut pan or line a baking sheet with parchment paper.
In medium bowl, stir all-purpose flour, baking powder, pumpkin pie spice, salt, and baking soda together in a bowl; set aside.
In bowl of stand mixture, beat butter until light and fluffy, about 2 minutes. Scrape sides. Add brown sugar and beat until well combined, another 2 minutes. Scrape sides again and add pumpkin puree; mix on medium speed until well combined.
In a separate bowl, beat eggs and milk until well combined. With mixer running on medium low speed, slowly add half of the egg mixture and beat until well combined. Scrape sides, then add remaining egg mixture and beat until mixed.
With mixer running, spoon flour mixture on large spoonful at a time until fully combined. Scrape sides again (lots of scraping, right?), then beat on medium one more minute to ensure all ingredients are well mixed. Batter will be very thick.
Spoon into a a pastry bag or large plastic storage bag with corner snipped off. Squeeze bag to fill wells of donut pan or to pipe donut shapes onto a prepared baking sheet.
Bake in preheated oven until donuts spring back when touched, 12 to 14 minutes. Transfer to a cooling rack.
To make the glaze, heat confectioners sugar, pumpkin pie spice, heavy cream, vanilla and hazelnut extract over low eat in small saucepan, whisking continuously until glaze is warm and there are no lumps. Turn off heat but keep glaze in pan.
When donuts are cool enough to handle, dip in warm glaze. Allow excess to drip off back into pan, and return to cooling rack to dry. Sprinkle with hazelnut meal, if desired.
Recipe can easily be doubled. Serve immediately. If not planning on serving immediately, do not glaze donuts. Store unglazed donuts in airtight container and add glaze before storing.